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Journal of the Optical Society of America B

Refined model for Talbot–Lau matter-wave optics with pulsed photodepletion gratings

Nadine Dörre, Philipp Haslinger, Jonas Rodewald, Philipp Geyer, Markus Arndt

Published Dec 18, 2014• 7 citations
Publisher

Abstract

We analyze time-domain Talbot–Lau interferometry of organic cluster beams that are exposed to pulsed photodepletion gratings in the vacuum ultraviolet. We focus particularly on the analysis of the complex (phase and absorption) character of the optical elements. The discussion includes the role of wavefront distortions due to mirror imperfections on the nanometer level and the effect of finite coherence in the diffraction gratings. This improved understanding of the interferometer allows us to extract new information on optical properties of anthracene and ferrocene clusters and to define conditions for future matter-wave experiments.

DOI
10.1364/josab.32.000114

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•Aug 5, 2021•1 citation
We analyze time-domain Talbot–Lau interferometry of organic cluster
beams that are exposed to pulsed photodepletion gratings in the vacuum ultraviolet.
We focus particularly on the analysis of the complex (phase and absorption)
character of the optical elements. The discussion includes the role of wavefront
distortions due to mirror imperfections on the nanometer level and the effect of
finite coherence in the diffraction gratings. This improved understanding of the
interferometer allows us to extract new information on optical properties of
anthracene and ferrocene clusters and to define conditions for future matter-wave
experiments.
We discuss modern developments in quantum optics with organic molecules, clusters and nanoparticles -- in particular recent realizations of near-field matter-wave interferometry. A unified theoretical description in phase space allows us to describe quantum interferometry in position space and in the time domain on an equal footing. In order to establish matter-wave interferometers as a universal tool, which can accept and address a variety of nanoparticles, we elaborate on new quantum optical elements, such as diffraction gratings made of matter and light, as well as their absorptive and dispersive interaction with complex materials. We present Talbot-Lau interferometry (TLI), the Kapitza-Dirac-Talbot-Lau interferometer (KDTLI) and interferometry with pulsed optical gratings (OTIMA) as the most advanced devices to study the quantum wave nature of composite matter. These experiments define the current mass and complexity record in interferometric explorations of quantum macroscopicity and they open new avenues to quantum assisted metrology with applications in physical chemistry and biomolecular physics.
We discuss the concept of an all-optical and ionizing matter-wave interferometer in the time domain. The proposed setup aims at testing the wave nature of highly massive clusters and molecules, and it will enable new precision experiments with a broad class of atoms, using the same laser system. The propagating particles are illuminated by three pulses of a standing ultraviolet laser beam, which detaches an electron via efficient single-photon absorption. Optical gratings may have periods as small as 80 nm, leading to wide diffraction angles for cold atoms and to compact setups even for very massive clusters. Accounting for the coherent and the incoherent parts of the particle–light interaction, we show that the combined effect of phase and amplitude modulation of the matter waves gives rise to a Talbot–Lau-like interference effect with a characteristic dependence on the pulse delay time.
We examine how partial coherence and wavefront curvature of beams affect interference fringes behind diffraction gratings. We simulate (1) the Talbot effect, (2) far-field diffraction, (3) Mach-Zehnader interferometers, (4) Talbot-Lau interferometers, and (5) Lau interferometers using a numerically efficient expression. We show how interference fringes in each case depend on the beam's initial width, its coherence width (transverse coherence length), and its wavefront curvature in directions both parallel and perpendicular to the grating bars. The separation between gratings and the rotational alignment of the gratings about the optical axis are also considered. The formula used for our simulations is derived using the mutual intensity function of a Gaussian Schell-model beam.
Weyl functions conveniently describe the evolution of wave coherences in periodic or quadratic potentials. In this work we use Weyl functions to study the ``Talbot-Lau effect'' in a time-domain matter-wave interferometer. A ``displacement diagram'' is introduced to analyze and calculate the matter-wave interference for an atomic cloud in a quadratic potential that interacts with a sequence of short optical standing wave pulses producing an atomic grating echo. Unlike previous treatments, this new approach allows the atomic ensemble to have an arbitrary initial phase-space distribution, and the standing wave grating vectors to span three dimensions. Several examples are discussed to illustrate the convenience of the diagrammatic technique including the following: a two-dimensional Talbot-Lau effect, the shift in the echo time and the recoil phase for the interferometer perturbed by a quadratic potential; and the realization of a time-domain ``Lau effect'' using a pulsed harmonic potential. The diagrammatic technique is applicable to diffraction gratings with arbitrary grating transmission functions. We conclude the paper with a general discussion on the Weyl function representations of matter-wave coherence, and relate the conservation of matter-wave coherence with the conservation of purity that distinguishes decoherence effects from dephasing effects.
Recent progress and future prospects of matter-wave interferometry with complex organic molecules and inorganic clusters are reviewed. Three variants of a near-field interference effect, based on diffraction by material nanostructures, at optical phase gratings, and at ionizing laser fields are considered. The theoretical concepts underlying these experiments and the experimental challenges are discussed. This includes optimizing interferometer designs as well as understanding the role of decoherence. The high sensitivity of matter-wave interference experiments to external perturbations is demonstrated to be useful for accurately measuring internal properties of delocalized nanoparticles. The prospects for probing the quantum superposition principle are investigated in the limit of high particle mass and complexity.
This thesis describes theoretical work carried out in connection with the high-mass matter-wave interference experiments at the University of Vienna. Its scope ranges from the simulation and analysis of experimental data to the proposal of a trapped interference scheme applicable to a variety of matter-wave platforms. The first main result of the thesis is the phase-space description of a near-field interferometer with any number of gratings. This theory is used to analyze a four-grating Talbot-Lau interferometer, in which passive compensation of low-frequency vibrations and of the Coriolis force are expected. The compensation is numerically confirmed and its effectiveness is compared to existing techniques. The second main result is the demonstration of Bragg diffraction of complex molecules on optical gratings, to which the author contributed the basic experimental design, simulations, and the interpretation of the data. This demonstration is a first step towards applying large momentum transfer coherent manipulation techniques to the interference of heavy molecules and clusters. The third main result is a new interference scheme for matter waves in toroidal confinement. The beam splitting and recombination in this scheme rely on the free evolution in the waveguide and require no interaction with the matter waves. The scheme is within reach of state-of-the-art experiments with Bose-Einstein condensates, where it could be used to measure weak atom-atom interactions or magnetic field gradients.